High-Performance Thin-Layer Chromatographic Method for the Estimation of Benzyl Isothiocyanate in Salvadora persica Root Extract and Dental Care Herbal Products

JPC – Journal of Planar Chromatography – Modern TLC - A novel, simple, and sensitive high-performance thin-layer chromatography (HPTLC) method has been successfully developed and...     

Targeted Delivery of Anticancer Drug Loaded Charged PLGA Polymeric Nanoparticles Using Electrostatic Field

Pure positive electrostatic charges (PPECs) show suppressive effect on the proliferation and metabolism of invasive cancer cells without affecting normal tissues. PPECs are used for the delivery of drug-loaded polymeric nanoparticles (DLNs) capped with negatively charged poly(lactide-co-glycolide) (PLGA) and Poly(vinyl-alcohol) PVA into the tumor site of mouse models. The charged patch is installed on top of the skin in the mouse models' tumor region, and the controlled selective release of the drug is assayed by biochemical, radiological, and histological experiments on both tumorized models and normal rats' livers. It is found that DLNs synthesized by PLGA show great attraction to PPECs due to their stable negative charges, which would not degrade immediately in blood. The burst and drug release after less than 48h of this synthesized DLNs are 10% and 50%, respectively. These compounds can deliver the loaded-drug into the tumor site with the assistance of PPECs, and the targeted-retarded release will take place. Hence, local therapy can be achieved with much lower drug concentration (conventional chemotherapy [2 mg kg⁻¹] versus DLNs-based chemotherapy [0.75 mg kg⁻¹]) with negligible side effects in non-targeted organs. PPECs have many potential clinical applications for advanced-targeted chemotherapy with the lowest discernible side effects.     

Global Exponential Stability in Discrete-time Analogues of Delayed Cellular Neural Networks

A novel method called semi-discretization is employed in the formulation of discrete-time analogues of nonlinear delayed differential equations modelling cellular neural networks. The dynamical characteristics of the discrete-time analogues are studied. When the network parameters satisfy certain sufficient conditions which are independent of the delays, the discrete-time analogues for any choice on the discretization step-size are shown to be globally exponentially stable. The sufficient conditions are obtained by employing an appropriate form of Lyapunov sequences and these conditions correspond to those which have been obtained in the literature for the global exponential stability of continuous-time delayed cellular neural networks. Several examples and computer simulations are given to support our results and to demonstrate some of the advantages of the discrete-time analogues in numerically simulating their continuous-time counterparts.     

Modeling on an ecological food chain with recycling

We propose two nutrient-phytoplankton models with instantaneous and time delayed recycling, investigate the dynamics and examine the responses to model complexities. Instead of the familiar specific uptake rate and growth rate functions, we assume only that the nutrient uptake and phytoplankton growth rate functions are positive, increasing and bounded above. We use geometrical and analytical methods to find conditions for the existence of none, one, or at most two positive steady states and analyze the stability properties of each of these equilibria. With the variation of parameters, the system may lose its stability and bifurcation may occur. We study the occurrence of Hopf bifurcation and the possibility of stability switching. Numerical simulations illustrate the analytical results and provide further insight into the dynamics of the models, biological interpretations are given.     

On the Filling Invariants at Infinity of Hadamard Manifolds

We study the filling invariants at infinity div _k for Hadamard manifolds defined by Brady and Farb [ Trans. Am. Math. Soc. 350(8) (1998), 3393–3405]. Among other results, we give a positive answer to the question they posed: whether these invariants can be used to detect the rank of a symmetric space of noncompact type.     

On the stability of the solitary waves to the rotation Benjamin‐Ono equation

In this paper, we study several aspects of solitary wave solutions of the rotation Benjamin‐Ono equation. By solving a minimization problem on the line, we construct a family of even travelling waves ψ_c,γ. We then prove the uniqueness of even ground states associated with large speed and their orbital stability. Note that this improves the results in Esfahani and Levandosky, where only the stability of the set of ground states is proven.     

Coexistence of domains of attraction of nonautonomous neural networks with time-varying delays

This paper presents new dynamical behavior, i.e., the coexistence of 2^N domains of attraction of N-dimensional nonautonomous neural networks with time-varying delays. By imposing some new assumptions on activation functions and system parameters, we construct 2^N invariant basins for neural system and derive some criteria on the boundedness and exponential attractivity for each invariant basin. Particularly, when neural system degenerates into periodic case, we not only attain the coexistence of 2^N periodic orbits in bounded invariant basins but also give their domains of attraction. Moreover, our results are suitable for autonomous neural systems. Our new results improve and generalize former ones. Finally, computer simulation is performed to illustrate the feasibility of our results.     

Global existence for the nonlinear fractional Schrödinger equation with fractional dissipation

We consider the initial value problem for the fractional nonlinear Schrödinger equation with a fractional dissipation. Global existence and scattering are proved depending on the order of the fractional dissipation.     

Enhanced Directed Random Walk for the Identification of Breast Cancer Prognostic Markers from Multiclass Expression Data

Artificial intelligence in healthcare can potentially identify the probability of contracting a particular disease more accurately. There are five common molecular subtypes of breast cancer: luminal A, luminal B, basal, ERBB2, and normal-like. Previous investigations showed that pathway-based microarray analysis could help in the identification of prognostic markers from gene expressions. For example, directed random walk (DRW) can infer a greater reproducibility power of the pathway activity between two classes of samples with a higher classification accuracy. However, most of the existing methods (including DRW) ignored the characteristics of different cancer subtypes and considered all of the pathways to contribute equally to the analysis. Therefore, an enhanced DRW (eDRW+) is proposed to identify breast cancer prognostic markers from multiclass expression data. An improved weight strategy using one-way ANOVA (F-test) and pathway selection based on the greatest reproducibility power is proposed in eDRW+. The experimental results show that the eDRW+ exceeds other methods in terms of AUC. Besides this, the eDRW+ identifies 294 gene markers and 45 pathway markers from the breast cancer datasets with better AUC. Therefore, the prognostic markers (pathway markers and gene markers) can identify drug targets and look for cancer subtypes with clinically distinct outcomes.